Beardy, you should spell check your guide (Achievement is misspelled just about every time and should be capitalized too).
For the hidden sign, it might help to point out that the dead end is on the lower-left corner of the map. Other dead ends appear on the map but can't actually be driven into.
And with the Jeffrey statue, note that the Back button must be pressed several times repeatedly. The statue advances one animation frame per button press.
The vehicle must actually be damaged in order for the Achievement to pop. Drive into a few walls and get the hood dented first.
For Survival, the Achievement will pop on the fourth lap on the Beginner circuit. You don't need to do anything special.
The Karaoke Achievement pops when the song completely ends on any of the circuits.